Rewrite as a simplified fraction. ${0.\overline{59} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 59.5959...\\ 1x &= 0.5959...\end{align*}}$ Subtracting the two equations, we have: ${99x = 59}$ ${x = \dfrac{59}{99}} $